A Robust Reorder-Time/Order-Quantity Policy Under Invisible Stock Loss

Inventory record inaccuracy has significant negative impacts on the performance of inventory management. We investigate a robust replenishment problem for an inventory system under inventory record inaccuracy caused by invisible stock loss, with the objective of minimizing the sum of the inventory holding cost, the backorder cost, and the materials transportation cost. First, we develop a recursive algorithm to estimate the probability distribution of the physical inventory levels. Based on this probability distribution, a robust myopic reorder-time/order-quantity (RTQ) policy is designed, which determines the robust reorder time and the robust replenishment quantity. Theoretical analysis and numerical experiments reveal some managerial insights of the proposed RTQ policy and the classical (r, Q), (s, S), and (R, S) policies: 1) if there exist invisible stock loss and inaccurate inventory record, the inventory system will be trapped into the zero-service state (i.e., the inventory level becomes less than or equal to zero with probability one) in finite time under the classical policies and 2) if the probability distribution of inventory record error is known exactly, the RTQ policy prevents the inventory system from being trapped into the zero-service state and maintains a high service level, even if we do not make any audit of its physical inventory level.